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    "### 解的存在性\n",
    "对于线性方程组$Ax=b$,若系数矩阵与增广矩阵的秩相等时，方程组有解；否则无解。\n",
    "\n",
    "\n",
    "### 行满秩矩阵一定有解\n",
    "对于列矩阵函数$Ax=y$,行满秩时，该列矩阵函数为满射，故一定存在解。\n",
    "\n",
    "\n",
    "### 齐次线性方程组\n",
    "对于线性方程组$Ax=b$，当$b=0$时，此时称为齐次线性方程组。齐次线性方程组的解集null(A)称为零空间。\n",
    "求解线性方程组$Ax=b$的过程可分成2步。第一步为求解齐次线性方程组的解空间null(A),第二步为求特解p,\n",
    "非齐次线性方程组的解空间为：$p+null(A)$\n",
    "\n",
    "### 秩零定理\n",
    "对于矩阵$A=(a_{ij})_{m\\times n}$,假定rank(A)=r。则有：rank(null(A))+r=n。\n",
    "翻译为线性方程语言：rank(定义域)=rank(值域)+rank(null(A))"
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